Image Ray Time to Depth
Conversion and Model Ray
Applications
Eduardo Filpo
Niterói
6/9/2012
Acknowledgements
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Covered Topics
• Time migration
• Image ray time-to-depth conversion
– Seismic sections
– Interval velocity in time
• Model rays
– Definition
– Applications
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Introduction
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
depth image
seismic model
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
velocity
density
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
velocity
density
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
velocity
density
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
velocity
density
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
velocity
density
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
velocity
density
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
velocity
depth migrated image
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
velocity
depth migrated image
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
velocity
depth migrated image
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
velocity
depth migrated image
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
velocity
depth migrated image
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
velocity
time migrated image
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
velocity
time migrated image
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
velocity
time migrated image
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
velocity
time migrated image
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
velocity
time migrated image
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
velocity
time migrated image
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
velocity
depth migrated image
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Kirchhoff migration
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Simple model for migration
seismic model
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Simple model for migration
velocity model (masked)
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Traveltime computation
(wavefront propagation)
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Traveltime computation
(wavefront propagation)
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Traveltime computation
(ray tracing)
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Traveltime computation
(ray tracing)
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Display and Notation
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
time
A0 , t
ZO data
A0 , t 0 
V x ,z
depth
velocity model
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
time
A0 , t
ZO data
I x ,z
depth
depth migrated image
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
time
A , 
time migrated image
A x , z 
depth
converted image
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
ZO data
A0 , t 0 
velocity model
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
ZO data
velocity model (masked)
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
point diffractor A
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
rays
A
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
diffraction curve
A
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
point diffractor B
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
rays
B
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
diffraction curve
B
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
C
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
C
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
diffraction curve
C
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
D
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
D
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
diffraction curve
D
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
E
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
E
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
diffraction curve
E
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
zero offset section
depth migrated section
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
zero offset section
seismic model
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
diffraction curves
A
C
B
SEG Honorary Lecture 2012
D
E
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Kirchhoff time migration
and
Image ray concept
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
D
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
D
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
E
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
diffraction curves
D
E
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
hyperbolas
D
E
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
hyperbolas
D
E
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
hyperbolas apex
D
E
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
hyperbolas apex
D
rays connecting
diffractors with
hyperbolas apex
E
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
D
E
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
D
E
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
hyperbolas apex
rays connecting
diffractors with
hyperbolas apex
D
E
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
wavefront
E
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
wavefront
E
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
wavefront
E
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
wavefront
E
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
wavefront
E
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Minimum time ray
E
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
E'
Minimum time ray
E
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
✔
Minimum time ray
Emerges vertically at the surface
✔
Connects diffraction point with hyperbola
apex.
✔
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Image Ray
Obeys Snell's law
✔
Starts vertically at the surface
✔
Connects the hyperbola apex with the
diffraction point.
✔
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
t
Image Ray
y
x
z
SEG Honorary Lecture 2012
Original from Peter Hubral,
Time migration – some ray theoretical
aspects: Geophysical Prospecting, 1977
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Kirchhoff Depth Migration
t=d  M , 

Diffraction surface
M
SEG Honorary Lecture 2012
∂ A0
 ,t 
I  M =∫ w  M , 

∣
d

∂t
t=  M , 

d
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Kirchhoff Depth Migration
t=d  M , 

Diffraction surface
Tygel et all, 1996,
A Unified approach to 3-D
seismic reflection imaging,
Part II: Theory
M
SEG Honorary Lecture 2012
∂ A0
 ,t 
I  M =∫ w  M , 

∣
d

∂t
t=  M , 

d
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Kirchhoff Time Migration
t=d  M , 

Diffraction surface
M
SEG Honorary Lecture 2012
∂ A0
 ,t 
I  M =∫ w  M , 

∣
d

∂t
t=  M , 

d
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Kirchhoff Time Migration
t=d  M , 

N
Diffraction surface
∂ A0
 ,t 
I  M =∫ w  M , 

∣
d

∂t
t=  M , 

d
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Kirchhoff Time Migration
N



4∣4∣
−
 N
∣ ∣


−

N
t hyp =  2
2
t hyp =   V rms2
2
V rms
Hyperbolic traveltime


∂
A


∂
A

,t, t 
0
0

N=
=∫
AA N
∣t =t d d 

∫ww N ,  ∂∂tt ∣t=t
hyp hyp
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Kirchhoff Time Migration
N
Image ray
M
SEG Honorary Lecture 2012



4∣4∣
−
 N
∣ ∣


−

N
t hyp =  2
2
t hyp =   V rms2
2
V rms
Hyperbolic traveltime


∂
A


∂
A

,t, t 
0
0

N=
=∫
AA N
∣t =t d d 

∫ww N ,  ∂∂tt ∣t=t
hyp hyp
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Comments
• Only examples are 2D
• Pre-stack time migration
• Common-offset sections
• Apex of zero-offset hyperbolas
• Validity depends on velocity variation
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
complex
none
Increasing structural
complexity
Validity of time migration
PreStack
Time
Migration
Poststack
time
migration
none
PreStack
Depth
Migration
Poststack
depth
migration
strong
Increasing lateral velocity variation
SEG Honorary Lecture 2012
time to depth Liner
conversion
and model
ray applications
ModifiedImage
fromray
Christopher
(Leading
Edge,
February
99)
Eduardo Filpo
Time to depth conversion
using image rays
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Image-ray time-to-depth
conversion
A  , 
A  x , z
Time migrated section
SEG Honorary Lecture 2012
Depth converted section
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Image-ray time-to-depth
conversion
A  x , z
A  , 
V  x , z
SEG Honorary Lecture 2012
Depth
velocity model
is necessary !
Image ray time to depth conversion and model ray applications
Eduardo Filpo
time
A  , 
depth
V  x , z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
time
A  ,
depth
V  x , z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
time
A  , 
depth
V  x , z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
time
A  , 
depth
V  x , z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
time
A  , 
depth
V  x , z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
time
A  , 
depth
A x , z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Depth migrated image
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Vertical stretching
Time-to-depth conversion
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Image ray
Time-to-depth conversion
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Velocity model
1730 m/s
1813 m/s
1.5 km
1975 m/s
2 km
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Depth migrated image
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Vertical stretching
Time-to-depth conversion
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Image ray
Time-to-depth conversion
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Field data example
Depth migration
SEG Honorary Lecture 2012
Time-to-depth conversion
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Field data example
Depth migration
SEG Honorary Lecture 2012
Time-to-depth conversion
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Field data example
Depth migration
SEG Honorary Lecture 2012
Time-to-depth conversion
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Field data example
Depth migration
SEG Honorary Lecture 2012
Time-to-depth conversion
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Field data example
Depth migration
SEG Honorary Lecture 2012
Time-to-depth conversion
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Field data example
Depth migration
SEG Honorary Lecture 2012
Time-to-depth conversion
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Field data example
Depth migration
SEG Honorary Lecture 2012
Time-to-depth conversion
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Instructive example
Seismic Model
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Instructive example
Time migrated section
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Instructive example
Image ray conversion
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Instructive example
Vertical Stretching
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Summary
V  x , z
Velocity model
A  , 
Time migrated
section
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Step 1: trace imaging rays
V  x , z
A  , 
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Step 2: collect amplitudes
V  x , z
A  , 
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Step 3: interpolate amplitudes
V  x , z
A  , 
SEG Honorary Lecture 2012
A  x , z
Image ray time to depth conversion and model ray applications
Eduardo Filpo
complex
none
Increasing structural
complexity
Validity of time to depth
conversion
PreStack
Time
Migration
Poststack
time
migration
none
PreStack
Depth
Migration
Poststack
depth
migration
strong
Increasing lateral velocity variation
SEG Honorary Lecture 2012
time to depth Liner
conversion
and model
ray applications
ModifiedImage
fromray
Christopher
(Leading
Edge,
February
99)
Eduardo Filpo
complex
none
Increasing structural
complexity
Validity of time to depth
conversion
PreStack
Time
Migration
Poststack
time
migration
none
PreStack
Depth
Migration
Poststack
depth
migration
strong
Increasing lateral velocity variation
SEG Honorary Lecture 2012
time to depth Liner
conversion
and model
ray applications
ModifiedImage
fromray
Christopher
(Leading
Edge,
February
99)
Eduardo Filpo
complex
PreStack
Time
Migration
PreStack
Depth
Migration
Time-to-depth
conversion zone
none
Increasing structural
complexity
Validity of time to depth
conversion
Poststack
time
migration
none
Poststack
depth
migration
strong
Increasing lateral velocity variation
SEG Honorary Lecture 2012
time to depth Liner
conversion
and model
ray applications
ModifiedImage
fromray
Christopher
(Leading
Edge,
February
99)
Eduardo Filpo
complex
PreStack
Time
Image
Migration
ray
Time-to-depth
conversion zone
none
Increasing structural
complexity
Validity of time to depth
conversion
Poststack
time
migration
none
PreStack
Depth
Migration
Poststack
depth
migration
strong
Increasing lateral velocity variation
SEG Honorary Lecture 2012
time to depth Liner
conversion
and model
ray applications
ModifiedImage
fromray
Christopher
(Leading
Edge,
February
99)
Eduardo Filpo
Time-to-depth conversion
of interval velocities
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
From a time migration velocity
field to a depth velocity model
V rms  , 
V  ,

d  V² rms 
d
SEG Honorary Lecture 2012
V x , z
rays ?
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Ray tracing
dx
=v² p x
dt
dp x
1 ∂V
=−
dt
v ∂x
dz
=v² p z
dt
dp z
1 ∂V
=−
dt
v ∂z
The velocity and its gradient are needed!
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Solution
• Image rays are vertical at the surface z=0
• Change of coordinates:
[ ] [ ][ ]
∂V
∂
∂x = ∂x
∂V
∂
∂z
∂z
SEG Honorary Lecture 2012
∂
∂x
∂
∂z
∂V
∂
∂V
∂
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Solution
• Image rays are vertical at the surface z=0
• Change of coordinates:
[ ] [ ][ ]
∂V
∂
∂x = ∂x
∂V
∂
∂z
∂z
∂
∂x
∂
∂z
∂V
∂
∂V
∂
wavefronts
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Wavefront construction

Downgoing plane wave
=0
z=0
,x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Wavefront construction

Initial conditions:
∂
∂
∂
∂
1
=1,
=0 ,
= p x =0,
= pz =
∂x
∂z
∂x
∂z
v
=0
z=0
,x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Wavefront construction

Rays with step: dt=
d
2
=0
,x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Wavefront construction

Rays with step: dt=
d
2
,x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Wavefront construction

,x
d
d
, z=z  ,t=

Wavefront: x=x  , t=
2
2
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Wavefront construction

=d 
,x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Wavefront construction

Rays with step: dt=
d
2
=d 
,x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Wavefront construction

Rays with step: dt=
d
2
=d 
,x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Wavefront construction

,x
Wavefront: x=x  ,t=d  , z=z  ,t =d 
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Wavefront construction

=2d 
,x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Wavefront construction

Rays with step: dt=
d
2
=2d 
,x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Wavefront construction

Rays with step: dt=
d
2
=2d 
,x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Wavefront construction

=3d 
,x
z
Wavefront: x=x  ,t=
SEG Honorary Lecture 2012
3d 
3d 
 , z=z  ,t=

2
2
Image ray time to depth conversion and model ray applications
Eduardo Filpo

V  , 

x
Illustrative model
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo


x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
On the application
of the
model ray concept
density
velocity
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
time
A 0  , t
Zero-offset section
depth
V x , z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
time
A  , 
Time migrated section
depth
V x , z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Curved line in time
Straight line in depth
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
time
depth
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Model ray

Model ray
, x
Vertical trajectory
in depth
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Model ray

Minimum of
diffraction curve
, x
z
SEG Honorary Lecture 2012
Point
diffractor
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Model ray

Hyperbola
apex
, x
z
SEG Honorary Lecture 2012
Point
diffractor
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Model ray

Virtual trajectory
of the hyperbola apex
, x
Downgoing
diffractor
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Model ray

Virtual trajectory
of the hyperbola apex
, x
Downgoing
diffractor
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Model ray

Virtual trajectory
of the hyperbola apex
, x
Downgoing
diffractor
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Model ray

Virtual trajectory
of the hyperbola apex
, x
Downgoing
diffractor
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Model ray

Virtual trajectory
of the hyperbola apex
, x
Downgoing
diffractor
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Connection with image rays

Model ray
, x
Image rays
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
time
A  ,
Image ray
time-to-depth
conversion
time
A  ,
Image ray
depth
A  x , z
time-to-depth
conversion
time
Model ray
I  x , z
depth
depth-to-time
conversion
time
I  ,
Model ray
I  x , z
depth
depth-to-time
conversion
Dualism
Model in
Depth
Image in
Time
Image
rays
Vertical
lines
Vertical
lines
Model
rays
Eikonal equations
Depth
domain
Time
domain
2
2
   
 
 
∂
∂
1

= 2
∂x
∂z
V  x , z
2
2
∂z
1
∂z
 2
=1
∂
V  ,  ∂
Equations for wavefronts
construction by Huygens's principle
Depth
domain
Time
domain
2
2
   
 
 
∂x
∂z
2

=V  x , z
∂
∂
2
2
∂
∂
2
V  , 
=1
∂z
∂z
Sava, P.C., Fomel, S., 2001, 3-D traveltime computation using
Huygens wavefront tracing, Geophysics, v. 66, no. 3, pp. 883-889.
Equations for wavefronts
construction by Huygens's principle
Depth
domain
Time
domain
2
2
   
 
 
∂x
∂z
2

=V  x , z
∂
∂
2
2
∂
∂
2
V  , 
=1
∂z
∂z
Silva, E.F.F., Portugal, R., Vicentini, A., 2009, Model rays for
depth-to-time conversion, 11th International Congress of the
Brazilian Geophysical Society.
“wavefront” construction in time
2
 
2
 
∂
∂
2
V  , 
=1
∂z
∂z
“Wavefront” construction in time

=0
z=0
,x
Forward “wavefront”
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
“Wavefront” construction in time

First step: straight model rays
,x
z=0
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
“Wavefront” construction in time

“wavefront”: = x , z=dz, = x , z=dz
,x
z=0
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
“Wavefront” construction in time

,x
z=dz
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
“Wavefront” construction in time

Second step: Huygens's principle
,x
z=dz
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
“Wavefront” construction in time

,x
z=dz
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
“Wavefront” construction in time

“Wavefront”: = x , z=2dz, =x , z=2dz
,x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
“Wavefront” construction in time

,x
z=2dz
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
“Wavefront” construction in time

,x
z=2dz
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
“Wavefront” construction in time

“Wavefront”: = x , z=2dz, =x , z=2dz
,x
z=2dz
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
“Wavefront” construction in time

,x
z=3dz z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Applications of model rays
• Time-to-depth conversion
• Depth-to-time conversion
• Synthetic seismograms
• Hybrid migration
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Applications of model rays
• Time-to-depth conversion
• Depth-to-time conversion
• Synthetic seismograms
• Hybrid migration
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Synthetic seismogram
example
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Velocity model
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Velocity model
Fictitious well
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Time migrated section
Synthetic
seismogram
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Time migrated section
Model-ray
synthetic
seismogram
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
SEG Honorary Lecture 2012
time
depth
Detail
Image ray time to depth conversion and model ray applications
Eduardo Filpo
time
depth
Detail
z≈5 Km
 x≈0.5 Km
Hybrid migration
Hybrid migration algorithm

,x
z
SEG Honorary Lecture 2012
Output seismic trace.
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Hybrid migration

Model ray.
,x
z
SEG Honorary Lecture 2012
Output seismic trace.
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Hybrid migration

Minimum time
,x
z
SEG Honorary Lecture 2012
Sample
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Hybrid migration

Hyberbolas
,x
z
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
time
Zero offset section
depth
Seismic model
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Time migrated section
“Hybrid” migrated section
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
time
Time migrated section
depth
“Hybrid” migrated section
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
A more realistic
example
Velocity model
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Velocity model
4 Km
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Velocity model
3 Km
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Velocity model
1500 m/s
4000 m/s
SEG Honorary Lecture 2012
3200 m/s
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Reflectivity model
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Zero offset section
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Depth migration
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Time migration
Vertical T2D conversion
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Hybrid migration
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Depth migration
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Time migration
Vertical T2D conversion
125 m
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Time migration
Vertical T2D conversion
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Hybrid migration
SEG Honorary Lecture 2012
Image ray time to depth conversion and model ray applications
Eduardo Filpo
Conclusion
• The concept of model rays
• Algorithm to trace model rays
• Applications of model rays
• Examples
Acknowledgements
I would like to thank SEG Busisness Office members,
in special Judy Wall for making all arrangements of this tour.
I would like to thank all my colleagues from PETROBRAS,
in special Claudio Guerra for preparing the realistic synthetic
dataset, Rodrigo Fernandes for the technical support in
Java programming, and Neiva Zago for providing conditions
to prepare this presentation.
Acknowledgements
Many thanks to the co-authors:
Armando Vicentini
José Carbonesi
Neiva Zago
Paulo Miranda Cunha
Rodrigo Portugal